Graph the inequality. 

3x + y ≤ 5



To graph a linear inequality in two variables x and y when the coefficient of y is not a zero.



 1. Write the given inequality as an equivalent inequality that has y alone on one side.

      3x + y ≤ 5

           y ≤ -3x + 5

              

 2. Graph the related linear equation. Use a dashed line if the inequality involves < or >. Use solid line if the inequality involves ≤ or ≥.



     graph y = -3x + 5. Since the inequality symbol used is ≤, use

     solid line.







 3. Test a point in each half-plane to see which satisfies the inequality.



       y ≤ -3x + 5, Test (0,0) when x = 0 and y = 0



       0 ≤ 0 + 5

       0 ≤ 5   ---------> true 



 4. Shade the appropriate half-plane.

    Since (0,0) satisfies the inequality that means you shade where the 

    (0,0) is located (the left side of the line formed)





The graph looks like this:









Remember to use solid line and shade the left side of the line.



 

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